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Mirrors > Home > ILE Home > Th. List > tgidm | Unicode version |
Description: The topology generator function is idempotent. (Contributed by NM, 18-Jul-2006.) (Revised by Mario Carneiro, 2-Sep-2015.) |
Ref | Expression |
---|---|
tgidm |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tgvalex 13183 |
. . . . 5
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2 | eltg3 13190 |
. . . . 5
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3 | 1, 2 | syl 14 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | uniiun 3937 |
. . . . . . . . . 10
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5 | simpr 110 |
. . . . . . . . . . . . 13
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6 | 5 | sselda 3155 |
. . . . . . . . . . . 12
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7 | eltg4i 13188 |
. . . . . . . . . . . 12
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8 | 6, 7 | syl 14 |
. . . . . . . . . . 11
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9 | 8 | iuneq2dv 3905 |
. . . . . . . . . 10
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10 | 4, 9 | eqtrid 2222 |
. . . . . . . . 9
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11 | iuncom4 3891 |
. . . . . . . . 9
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12 | 10, 11 | eqtrdi 2226 |
. . . . . . . 8
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13 | inss1 3355 |
. . . . . . . . . . . 12
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14 | 13 | rgenw 2532 |
. . . . . . . . . . 11
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15 | iunss 3925 |
. . . . . . . . . . 11
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16 | 14, 15 | mpbir 146 |
. . . . . . . . . 10
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17 | 16 | a1i 9 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | eltg3i 13189 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | 17, 18 | sylan2 286 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | 12, 19 | eqeltrd 2254 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | eleq1 2240 |
. . . . . . 7
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22 | 20, 21 | syl5ibrcom 157 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 22 | expimpd 363 |
. . . . 5
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24 | 23 | exlimdv 1819 |
. . . 4
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25 | 3, 24 | sylbid 150 |
. . 3
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26 | 25 | ssrdv 3161 |
. 2
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27 | bastg 13194 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
28 | tgss 13196 |
. . 3
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29 | 1, 27, 28 | syl2anc 411 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | 26, 29 | eqssd 3172 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 ax-un 4429 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-iun 3886 df-br 4001 df-opab 4062 df-mpt 4063 df-id 4289 df-xp 4628 df-rel 4629 df-cnv 4630 df-co 4631 df-dm 4632 df-iota 5173 df-fun 5213 df-fv 5219 df-topgen 12644 |
This theorem is referenced by: tgss3 13211 txbasval 13400 |
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